1. Field of the Invention
The invention lies in the field of metrology and relates to a measurement system for determining six degrees of freedom of an object, in particular of a moving object, more specifically it serves for determining three position coordinates of a reference point of the object and three rotation angles (tilt, yaw- and roll angle) about three orthogonal axes which run through the object and which intersect, for example, in the reference point.
2. Description of Related Art
For determining the six degrees of freedom of an object, for example laser trackers, theodolites or theodolite-like measurement apparatus provided with distance meters are used, wherein direction and distance (polar coordinates) to a plurality of points marked with reflectors in known positions on the object are determined. From the measured coordinates of the points, the six degrees of freedom of the object relative to a predefined coordinate system are calculated, for example, relative to the coordinate system of the measurement apparatus. Since the marked points are sighted and measured consecutively, the methods are in particular suitable for stationary objects or for objects which move slowly.
According to known photogrammetric methods, an arrangement of light points arranged on the object in known positions (e.g. white or reflecting marks, points illuminated by light beams or reflectors or active light sources) are imaged from different positions by a plurality of cameras. The directions to the light points relative to the optical axis of the respective camera are determined from the positions of the light points on the images recorded by the cameras, and the position and orientation of the light point arrangement and, as the case may be, also the position and orientation of the camera(s) in a predefined coordinate system are determined from the total quantity of the data. Since such photogrammetric evaluation of the six degrees of freedom is only suitable for moving objects if a plurality of simultaneously operating, advantageously stationarily arranged and calibrated cameras is provided, the method is relatively demanding, in particular regarding the data quantities which are to be handled.
For this reason it is suggested in the patent document U.S. Pat. No. 5,440,392 (Metronor) to use only one camera. If at least three light points are arranged on the object, and a calibrated camera is used, the data obtained from a single camera picture allows determination of the six degrees of freedom of the light point arrangement relative to the camera, wherein, however, no great accuracy can be achieved regarding depth, i.e. regarding the distance between the camera and the light point arrangement. The object on which the light points are arranged, is a touch tool, for example. The touch tool is positioned on a point to be measured and position and orientation of the point to be measured are determined from the position and orientation of the touch tool.
For improving the accuracy of the depth measurement, it is suggested, in a subsequent publication U.S. Pat. No. 5,973,788 (Metronor), to combine the single camera with a distance measurement apparatus, a so-called laser rangefinder, i.e. an apparatus operating with a laser beam as a measurement beam and a reflector for the reflection of the measurement beam back into the distance measurement apparatus, wherein the reflector is provided on the object in addition to the light points to be detected with the camera. The reflector, which may simultaneously also be one of the light points to be detected by the camera, has a known position in the light point arrangement.
A measurement system for determining five degrees of freedom of an object relative to a predefined coordinate system is known from the patent document U.S. Pat. No. 6,667,798 (Leica Geosystems). The system serves in particular for determining the five degrees of freedom of a moving reflector or of a moving object on which the reflector is arranged. The measurement system comprises a laser tracker equipped with a distance measurement apparatus. The laser tracker directs a laser beam (measurement beam) to the reflector and follows or tracks the reflector, when moving, wherein the direction of the measurement beam relative to the tracker is detected. The reflector is a retroreflector (triple mirror-reflector or cube-corner prism) whose apical tip is replaced by an apical opening (triple mirror reflector) or an apical surface which is aligned parallel to the entry surface (cube-corner prism), wherein the apical opening or surface is smaller than the cross section of the measurement beam. Whilst a part of the measurement beam is reflected back into the distance measurement apparatus and is analysed with respect to the distance between the tracker and the reflector, another part of the measurement beam passes the reflector, exits this through the apical opening or surface, and hits a light-sensitive surface arranged behind the reflector, for example a CCD (charge coupled device, as provided in a digital camera) or PSD (position sensitive device) which is preferably arranged perpendicular to the reflector axis and with its center point lying on the reflector axis. The image coordinates (x, y) of the location at which the measurement part beam hits this surface and which can be read out from the light-sensitive surface, is a direct measure for the angle of incidence of the measurement beam into the reflector (spatial angle between measurement beam and reflector axis) or for the rotation angle of the reflector axis about two axes aligned perpendicular to the measurement beam (tilt and yaw angle or two degrees of freedom of the orientation of the reflector or object). Five degrees of freedom of the reflector or of the object relative to a tracker-related coordinate system can be computed from the measurement data of the tracker (two spatial angles of the measurement beam relative to a predefined zero direction of the tracker and distance between tracker and reflector) and from the measurement data of the light-sensitive surface behind the reflector (tilt and jaw angle of the reflector axis relative to the measurement beam).